TSTP Solution File: GEO011-3 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GEO011-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 16 20:34:15 EDT 2022
% Result : Unsatisfiable 0.20s 0.41s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 20
% Syntax : Number of formulae : 34 ( 11 unt; 5 typ; 0 def)
% Number of atoms : 176 ( 0 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 198 ( 59 ~; 123 |; 0 &)
% ( 16 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 8 ( 8 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 2 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 63 ( 57 !; 0 ?; 63 :)
% Comments :
%------------------------------------------------------------------------------
tff(colinear_type,type,
colinear: ( $i * $i * $i ) > $o ).
tff(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
tff(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
tff(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
tff(between_type,type,
between: ( $i * $i * $i ) > $o ).
tff(1,plain,
( colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
<=> colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
tff(3,plain,
colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Z: $i,Y: $i,X: $i] :
refl(
( ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
^ [Z: $i,Y: $i,X: $i] :
trans(
monotonicity(
rewrite(
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) ) )),
rewrite(
( ( between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
( ( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) )
<=> ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,axiom,
! [Z: $i,Y: $i,X: $i] :
( ~ colinear(X,Y,Z)
| between(X,Y,Z)
| between(Y,Z,X)
| between(Z,X,Y) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-1.ax',colinearity4) ).
tff(10,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(skolemize,[status(sab)],[11]) ).
tff(13,plain,
! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) ),
inference(modus_ponens,[status(thm)],[12,5]) ).
tff(14,plain,
( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
<=> ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension3) ).
tff(16,plain,
~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
( ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
<=> ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension2) ).
tff(19,plain,
~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
<=> ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(rewrite,[status(thm)],]) ).
tff(21,axiom,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO002-0.ax',lower_dimension1) ).
tff(22,plain,
~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ( between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(monotonicity,[status(thm)],[24]) ).
tff(26,plain,
( ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) )
<=> ( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
( ~ ! [Z: $i,Y: $i,X: $i] :
( between(Z,X,Y)
| between(Y,Z,X)
| between(X,Y,Z)
| ~ colinear(X,Y,Z) )
| between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
| between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
| between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
| ~ colinear(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
$false,
inference(unit_resolution,[status(thm)],[28,22,19,16,13,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO011-3 : TPTP v8.1.0. Bugfixed v1.2.1.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n016.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Wed Aug 31 04:59:47 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.20/0.41 % SZS status Unsatisfiable
% 0.20/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------